UA86820C2 - Method for development of independent multi-dimensional calibration models - Google Patents

Abstract

The invention relates to analytical instrument engineering and can be used for designing calibrating patterns of measuring devices for determining one or several secondary properties of an unknown sample on the basis of the measuring results of a plurality of the primary properties thereof. The inventive method consists in selecting a calibrating set for samples whose secondary properties are known and are defined by means of reference methods, in measuring the primary properties of each said sample by means of a reference device, in converting the measuring results into a form corresponding to the calibratable device, in forming a calibrating pattern enabling to define the analysed secondary properties of the unknown sample on the basis of the measurement of the plurality of primary properties thereof measured by means of the calibralable device. Said method is characterised in that the mathematics for the calibration translations are determined by selecting the combination of samples therefor and the primary properties of each sample are measured by the reference and calibratable devices. The selection of an independent multidimensional calibrating pattern is carried out by comparing the results and by using a method for verifying the accuracy thereof, thereby taking into account the non-linear differences of technical parameters of the calibratable and reference devices and the operating conditions.

Description

Changes in external conditions, as well as the technical characteristics of the measuring device, can significantly affect the results of measuring the primary properties of the samples, and as a result, the accuracy of determining the parameters that characterize the secondary properties of the analyzed samples. Therefore, several methods of creating calibration models that are not sensitive to changes in measurement conditions were proposed, as well as several ways of transferring calibration models between measuring devices, which allows taking into account differences in the technical characteristics of devices and not repeating the complex process of building a calibration model on each individual device.

There is a known method of creating multidimensional grading models (2, 3), which have little susceptibility to changes in the parameters of the device on which the measurements are made, as well as to changes in the external conditions under which the measurements take place, and to changes in other properties of the sample. In this method, to create a grading model, measurements of a large number of parameters that characterize the primary properties of the sample are carried out for each sample from the so-called grading set of samples with known secondary properties. The samples of the calibration set are selected in such a way that the other properties of the samples vary in the maximum possible range. In addition, when measuring the primary properties of samples from the calibration set, the parameters of the measuring device on which the calibration model is built are deliberately changed, for example, in the case of spectrometers, spectral distortions and changes in the amplitude of the measured signal are introduced.

The amount of change in device parameters when building a grading model is determined by the maximum possible amount of change in these parameters, which are expected between different devices during production or will occur during operation. In addition, a change in external conditions is introduced. Changes in device parameters or other measurement conditions can also be introduced not in the process of real measurements, but through mathematical transformations.

This method allows you to create a multidimensional grading model, which gives the results of the analysis of the secondary properties of the sample, which do not depend much on the conditions of measurements and the device on which these measurements were carried out, therefore, the grading model is created once and is used without changes on all devices of the same type.

Deliberately introducing the scatter of the data of the measurement results of the samples of the calibration set definitely makes the model more stable, and the area of applicability of the calibration constructed in this way is wider.

However, the accuracy of the results of the analysis using the grading model, which is created according to this method, will be reduced, because the model initially assumes a variation in the results of the measurement of the primary properties. In addition, the number of factors that influence the results of measurements is very large, and it is not always possible to build a mathematical model that takes into account the influence of all possible factors. Therefore, in order to build a full-fledged grading model that takes into account the influence of a large number of additional factors, it is necessary to conduct a huge number of measurements of samples of the grading set under different conditions, which makes the already complex process of creating a grading model even more time-consuming and long. The last disadvantage of the grading model created using this method is that the introduction of variations in the results of measurements of the samples of the grading set makes it difficult to assess the validity of the application of the grading model for the analysis of one or another unknown sample, which can lead to errors in the analysis of secondary properties. For example, it may be that a calibration model for determining the percentage of different chemical components in a sample will be used to analyze an unknown sample that consists of other components that are significantly different from the calibration set samples.

There is another approach to creating multidimensional calibration models, which does not attempt to build a universal calibration model that works on all devices and takes into account all possible factors that affect the results of measurements. Instead, in order for the calibration model built on one device, which works under the same conditions, to allow determining the secondary properties of samples based on the results of measurements of primary properties on another measuring device, which differs in terms of technical parameters and works under different conditions, specially developed methods are used transfer of gradations. in. Zpepk et al. (4) proposed a method of transferring a multidimensional calibration model between spectrometers, based on the transformation of spectral data measured on a calibrated instrument to a form equivalent to measurements on a reference instrument that was used to create a calibration model.

Determination of secondary properties of unknown samples is carried out after conversion of spectral data, directly using the calibration model created on the reference device.

First, the grading model is created on the reference spectrometer using methods of multivariate regression analysis (such as multi-linear regression of MI Y, regression of principal components of ROSA, or the method of fractional least squares RI 5), which are used to find relationships that connect known parameter values, which describe the secondary properties of the analyzed samples from the calibration set with the spectral characteristics of these samples measured on a reference instrument (for example, with absorption spectra). To transfer the graduation model to the graduated device, a set of samples for the transfer of graduations is used, also with known properties to be analyzed; for example, it may be part of the samples from a calibration set. The spectral characteristics of the samples from the calibration transfer set are measured both on the reference and on the calibrated devices. After that, by comparing the results of measurements of the spectral characteristics of the same samples on the reference and calibrated spectrometers, mathematical ratios are found that allow converting the spectral data measured on the calibrated instrument to a form equivalent to the results of measurements on the reference instrument. The found mathematical relations are used each time to perform transformations on the results of measuring the spectral characteristics of an unknown sample on a calibrated device. After that, the calibration model created on the reference spectrometer can be applied to determine the secondary properties of the unknown sample.

In more detail, the procedure for finding mathematical ratios for the transformation of spectral data looks like this. In the first step, the shift of wave numbers is determined. To determine the wave number shift, correlation coefficients are calculated between the spectral data measured on the reference device at a given wave number and the spectral data measured on the calibrated device at several values of the wave numbers closest to the given wave number. Next, it is assumed that the correlation coefficients are related by a quadratic relationship to the values of the wave numbers in the spectral data measured on the calibrated device. The coefficients of this quadratic dependence are determined by the method of least squares. The value of the wave number of the graduated device, at which the maximum of the quadratic dependence is reached, corresponds to the given value of the wave number of the reference device, from which we determine the spectral shift for each point in the spectral data of the reference device. This procedure for finding the spectral shift works well for devices with scanning diffraction gratings due to their design features.

After determining the spectral shift, a procedure of linear interpolation of spectral data measured on a calibrated instrument is carried out, where the value of the amplitude of the measured signal is found at given values of wave numbers, which correspond to the values of wave numbers in the reference spectral data. Next, the amplitude correction of the interpolated spectral data is carried out, finding the coefficients of the linear relationship between the interpolated spectral data and the reference spectral data by the method of least squares. For some values of the wave numbers, it is impossible to find the correction coefficients, since the value of the spectral data at these points is zero. This may be the result of mathematical processing of the original measurement results, for example, differentiation of spectral data; in this case, the correction amplitude factors for these wavenumbers are found by interpolation.

Thus, the result of this method of transfer of graduations is: the graduation model created on the reference device and the data necessary to perform the transformation of the results of measurements of spectral characteristics on the calibrated device into a form equivalent to the measurements on the reference device, which include the amount of the spectral shift and correcting the amplitude coefficients for each value of the wave numbers

The disadvantages of this method are: a narrow focus on spectrometers with scanning diffraction gratings and a large volume of calculations performed on a calibrated device when analyzing an unknown sample before comparing the measured spectral characteristics with a calibration model to determine interesting secondary properties. This increases the data processing time and requires high computing power, which can be significant when analyzing the product directly in the production process, where the speed of data acquisition is a key parameter. In addition, this method does not store data on the measurement results of the calibration set on the calibrated device, so it is impossible to assess the applicability of the calibration model for the analysis of an unknown sample, which limits the field of application of this method to those cases when it is known in advance that the unknown sample falls within the range of changes in spectral data, which is covered by the gradation set. The lack of data on the measurement results of the calibration set samples also does not allow to expand the calibration model by measuring additional calibration samples directly on the calibrated device, because in order to determine the samples that fall out of the calibration set, complete information on the measurement results of all the calibration set samples is required. Extending the gradation without such a check can lead to instability of the gradation model.

The most complete description of the methods of transferring graduation models is presented in (5i), where several different methods of transferring graduation models are described at once. Although this patent describes methods of transferring graduations between spectrometers, these methods can be easily transferred to any other instruments for the analysis of one or more secondary properties of an unknown sample based on the results of measuring a set of primary properties of this sample. The patent considers three main methods of transferring grading models from a reference device to a calibrated device. As in the method proposed in (4), a grading model based on spectral data is first created, measured on the reference instrument for a calibration set of samples with known properties to be analyzed. Then, a portion of the samples is selected from the calibration set and a calibration transfer set is created, which is measured on the calibration instrument and used to determine the calibration transfer ratios. For the reliable determination of calibration transfer ratios, samples from the calibration transfer set should provide a sufficient amount of information about the features of the results of spectral data measurements on different devices. Therefore, the number of these samples should not be less than the rank of the matrix of coefficients of the grading model created on the reference device. Further, the transfer of the grading model is carried out by comparing the spectral data measured on the reference and graduated device according to one of the proposed methods.

In the first method, called "classical" by the authors, it is assumed that for the samples from the set for the transfer of graduations, all analyzed secondary properties are known, for example, concentrations of components, samples of chemical components. Then the relationship between the measured spectral data and the known properties of the samples is determined by two different calibration models for the reference and calibrated device. This can be written in matrix form as

VI-SKI 4

Va-SKo-C(Ki-AK) 0) where Vi is the matrix of spectral data measured on the reference device, which has the dimension t X n;

B" is a similar matrix of spectral data measured on a calibrated device; n - the number of spectral points in the measurement results, t - the number of samples in the set for the transfer of graduations, C - the matrix of the properties of the samples (concentrations), which are determined, having the dimension т X s; c - the number of properties that are determined;

Ki is a reference calibrated model, Ko" is a corrected calibrated model, presented in the form of matrixes of coefficients having the dimension c X n. The matrix of correction coefficients has the form

AK-SYAV2-Bi) (2) where C" is the pseudo or generalized inverse matrix of sample properties (because the matrix C is non-square in general). Using expressions (1) and (2) we can find the spectral data that would be obtained by measuring the entire calibration set of samples on the calibration instrument, then building a new calibration model. Thus, the "classical" calibration transfer method uses the known properties of samples from the calibration transfer set to determine correction factors. These coefficients determine the relationship between secondary properties of the samples from the calibration transfer set and the primary properties of these samples measured on the calibrated instrument. Then, based on the known secondary properties of the samples of the complete calibration set, using the given correction factors, find the primary properties for each sample from the complete calibration set, emulating the measurement of the calibration dial on a graduated device comparing the calculated values of the primary properties of the samples of the calibration set and the known secondary properties of these samples, with the help of regression analysis methods, a new calibration model is created for the calibrated device, which is used further to determine the secondary properties of the unknown sample based on the results of measuring the primary properties of this sample on the calibrated device.

The classic method of transfer of calibrations can be used only if all the properties of the samples from the calibration set are accurately known, for example, there are accurate data on the concentrations of all chemical elements that make up the sample. In addition, the calibration transfer sample set is part of the samples from the full calibration set, for which all secondary properties must also be known. In addition, this method implicitly assumes that the carry-set-adjusted grading model has sufficient predictive accuracy and is robust, although no actual validation is performed. As experience shows |5|, this method is characterized by a relatively low probability of determining the properties of the sample.

In the case when there is no need to determine all the secondary properties of the samples, but only one specific property is of interest, for example, the protein content, in (5) it is proposed to use the "reverse" method of transfer of gradations. A modified "inverse" method was also proposed in |6)І. In this method, the volume of mathematical calculations is significantly reduced compared to the "classical" method, because the concentration matrix is degenerated into a vector "c" of dimension t, and the grading model is also described by a vector of coefficients "p" of dimension n. First, in a standard way, using a multivariate regression analysis, based on the calibration set of samples, a calibration model is created on the reference device, which determines the relationship connecting the matrix of spectral data or other primary properties of the samples from the set for transfer of calibrations measured on the reference device (Vi) and the secondary property of these samples, which is determined . c-NIVi (3)

Next, the same samples from the calibration set are measured on a calibrated instrument, and the coefficients of the calibration model are adjusted to obtain known characteristic values that describe the secondary properties of the samples from the calibration set. c-H2p2-Nag(p1--AB) (4)

As a result, the vector of coefficients of the new grading model can be expressed through the vector of coefficients of the reference grading model and the inverse matrices of the results of the measurement of the primary properties (spectral data) of the samples from the set for the transfer of graduations on the reference and graduated devices, respectively. p2-01-4(A2-A)C (5)

In contrast to the "classical" method of transferring graduations, in the "reverse" method, no correction is made of all the results of measuring the primary properties of the samples of the calibration set on the reference device in order to bring them to a form equivalent to the results of the measurement on the calibrated device. In this method, based on the measurements of the samples of the calibration transfer set, the adjusted coefficients of the calibration model are found, which are subsequently used to determine the secondary properties of the unknown sample. This method can be extended to the case when several properties of the sample are investigated simultaneously. Then vectors will be replaced by matrices.

The main advantage of this method of transferring gradations is that relatively low computing power is required for its implementation. Moreover, the result of the application of this method of transfer of graduations is the adjusted coefficients of the graduation model built on the reference device, which are directly used to determine the secondary properties based on the results of the measurement of the primary properties on the graduated device, which significantly reduces the time of analysis of an unknown sample.

However, to achieve high accuracy in determining the properties of unknown samples on a calibrated instrument, it is necessary to use a large number of samples in the calibration transfer set. The larger the sample set, the higher the accuracy. As in the "classical" method, in the "inverse" method there is no possibility to evaluate the applicability of the transferred calibration model for the analysis of an unknown sample measured on a calibrated instrument, because for this it is necessary to have information about the spectral data for all samples of the calibration set measured under conditions equivalent to conditions of measurement of an unknown sample.

The third method of transferring graduations, described in (5iI), the authors called the "direct" method. In this method, using the results of measuring the primary properties (spectral characteristics) of samples from the set for transferring graduations obtained on the reference and calibrated device, the matrix of the transformation of the measurement results is found ( P), which determines the functional relationship between the results of measuring the primary properties of an arbitrary sample on a reference device and the results of measuring the same sample on a calibrated device.

B-VVI (6)

After that, the primary properties of an arbitrary sample, measured on a calibrated device, can be brought to a form equivalent to the results of measuring this sample on a reference device.

Geo (7) go - the results of the measurement of the primary properties of the sample on a graduated device, and d1 - the result of mathematical transformation of the results of the measurement of the primary properties of the sample on the graduated device into a form equivalent to the results of the measurement on the reference device.

In this method, mathematical relationships connect each value of the primary properties of the sample, transformed into a form equivalent to the results of measurement on the reference device, with each value measured on the calibrated device. This means that each point in the spectral data transformed into a reference instrument view is a function of the spectral data at all points measured on the calibrated instrument. This makes the transfer of graduations the most accurate, but it is also the cause of one of the disadvantages of this method. Namely, that the conversion of spectral data using the "direct" method requires high computing power and can make the device significantly more expensive. The number of samples in the calibration transfer set should be at least equal to the rank of the spectral data matrix for the complete calibration set measured on the reference instrument, and the measurement result transformation matrix used in this method has the dimension n X n, where n is the number of spectral points at which measurements are made, and n, as a rule, is a large number and its value can exceed 100. In addition, every time before determining the secondary properties of the sample that are analyzed, it is necessary to carry out mathematical transformations of the measured data into the type of reference device, which can significantly increase analysis time.

It should be noted that in the described method of transferring grading models with the help of certain transformations, the primary properties of the samples measured on the graded device are brought to a form equivalent to the results of the measurement on the reference device, after which the grading model created is used to determine the secondary properties that are analyzed on the support device. Moreover, the calibration model created on a reference device must undergo a standard validation procedure |, which guarantees the stability of the model, but this is not a sufficient condition that this model is stable when analyzing the results of measurements obtained on a calibrated device and transformed into a form equivalent to the results of measurements on the support device. To do this, the measurement results of the unknown sample should be analyzed for the presence of outliers using outlier prediction statistics, such as

Mahalanobis, which requires information on the results of measurements of samples of a complete grading set, and not only data on constants in the mathematical ratios of the grading model. Therefore, in some cases, it is useful to have a separate "independent" grading model. By the term "independent model" we mean such a calibration model, which is created separately for each device being calibrated, takes into account its features, makes it possible to assess applicability for the analysis of one or another unknown sample, and guarantees stability. The independent calibration model can be expanded by simply measuring additional calibration samples on the calibrated device without using a reference device, for example, to correct the calibration model when the parameters of the device being calibrated change during operation (aging).

A known method of transferring graduation models between instruments (7|, also oriented towards the transfer of graduations between spectrometers. According to the set of essential features, this method is the closest to the claimed invention. This method includes: determination of the spectral transfer function of the reference spectrometer and the spectrometer that is calibrated, by measuring spectral data on both devices for a monochromatic light source; determination of correlation relations between the spectral transfer functions of the reference spectrometer and the spectrometer being calibrated, and finding mathematical ratios for converting the results of measurements on the reference device into a form equivalent to the results of measurements on the calibrated device; selection samples of the calibration set with known properties to be analyzed; measurement on the reference spectrometer of the spectral characteristics of each sample from the calibration set; conversion using the found ratios of spectroscopic data for the gradation samples of the set, measured on the reference spectrometer, in a form equivalent to the results of measurements of the samples of the calibration set on the calibrated spectrometer; and creating a calibration model for a calibrated spectrometer by determining, using regression analysis methods, the relationships between the known properties of the calibration set samples and the transformed spectral data.

The calibration model created on the calibrated device using this method is completely independent of the reference device. Moreover, this method makes it possible not to repeat the measurement of samples of the calibration set on each calibrated device, but uses the data measured on the reference device converted into the type of the device being calibrated. Such a calibration model can be easily supplemented and expanded by measuring additional calibration samples, directly on the calibrated device.

However, the ratios for converting the results of measurements carried out on a reference device into a form equivalent to measurements on a graduated device are established by comparing the responses of both devices to the same source of monochromatic light. Therefore, this method is suitable only for spectrometers, and cannot be used for instruments using other principles of analysis, when other non-spectroscopic primary properties of samples are measured. Note that in order to obtain a reliable transfer of gradations, a monochromatic source must have an unprecedentedly high stability. Such a source of radiation, as a rule, has a high cost and may not always be available. The main disadvantage of this method is that the use of only one monochromatic radiation line does not allow finding exact ratios for the transformation of spectral data. The theory of the spectral transfer function is developed for linear approximation. However, very often the variations in the characteristics of devices have a non-linear nature, for example, the wavelength shift in devices with scanning diffraction gratings (41.

Thus, the use of mathematical transformations obtained in this way can lead to incorrect results of spectral data transfer in case of non-linear changes in the characteristics of devices. In addition, this method of transferring graduations does not take into account variations in the intensity and radiation spectrum of polychromatic light sources in the graduated spectrometers themselves.

The task of this invention is to create an independent grading model for determining one or more secondary properties of an unknown sample based on the results of measurements of numerous primary properties of this sample, not necessarily spectral, which ensures high accuracy in determining the analyzed properties and takes into account non-linear differences in the technical parameters of the graded and reference devices and the influence of operating conditions, and in addition, provides the possibility of expansion and addition, by measuring additional calibration samples on the calibrated device.

The task is solved by creating independent multidimensional grader models, which includes a sequence of actions united by a single inventive idea.

The method includes the selection of a grading set of samples with known secondary properties determined by reference methods; measurement on the reference device of the primary properties of each of the samples of the calibration set with known secondary properties and transformation of the results of the measurement of the primary properties of the samples of the calibration set with the help of the transfer ratios of the graduations into the form as if the measurements were carried out on a calibrated device; creation of a grading model by finding with the help of regression analysis methods using the transformed data of grading ratios, which allow to determine the secondary properties of the unknown sample being analyzed, based on the results of measurements of a set of primary properties of this sample, carried out on a calibrated device, and differs in that the transfer ratio of the graduations are found by selecting a set of samples for the transfer of graduations, measuring the primary properties of each sample from the set for transferring graduations on the reference and calibrated devices and comparing, using the methods of multivariate regression analysis, the results of the measurements of the primary properties of the samples of the set for the transfer of graduations, obtained on the reference device, with the measurement results primary properties of the same samples obtained on a calibrated device, and the found calibration ratios are chosen as the optimal calibration model using the procedure for checking accuracy (in lidation).

The use of a set of samples for the transfer of calibrations allows you to take into account nonlinear changes in the characteristics of the devices, because several dependencies of changes in the primary properties are used to find the conversion ratios of the measurement results.

In addition, all the measurement results of the calibration set samples are converted into a form equivalent to the measurement results on the calibrated device and stored in the computer of the calibrated device. This makes the model created using this method completely independent of the measurements on the reference instrument, and allows, when measuring an unknown sample on a calibrated instrument, to analyze the falling data using emission prediction statistics, which guarantees high accuracy in determining the secondary properties being analyzed .

Various methods of selection of samples in the set for transfer of graduations are proposed.

Carrying out the accuracy check (validation) procedure at the final stage ensures that the built model meets the specified accuracy of the analysis of secondary properties of unknown samples. Calibration validation is carried out by comparing the secondary properties of samples, determining them from the results of measurements on a calibrated device using calibration ratios with direct results of measuring secondary properties using reference methods.

It is possible to expand the created grading model in order to increase the accuracy of the analysis and the stability of the model by supplementing the results of measurements of the primary properties of the samples of the grading set, transformed into a view as if the measurements were carried out on a calibrated device, with the results of measurements of the primary properties of additional grading samples with known secondary properties, carried out on calibrated device and finding mathematical correlations of calibration based on supplemented calibration data, and the created calibration model is completely independent from a similar calibration model built on a reference or any other device.

It is possible to transfer the supplemented calibration data to another device, including back to the reference device, after which a new calibration model is created, and the device on which additional calibration samples were measured acts as a new reference device.

In order to increase the stability of the created grading model, it is proposed to use emission prediction statistics and to exclude from the model the samples of the grading set that fall out before determining the grading ratios.

It is proposed to use the procedure of normalization of the results of measurements and reference data, which ensures a minimum error in the determination of the analyzed secondary properties and which allows taking into account the technical features of the device on which the measurements are carried out, as well as differences in sample preparation and the condition of the sample under study. The normalization procedure is a choice of one or another method of mathematical refinement. The criterion for the selection of reprocessing is the accuracy of the analysis of the secondary properties of the samples, which is provided by a graduated device with a graduation, during the creation of which this type of mathematical reprocessing was used. Quantitative parameters of the grading model validation procedure (for example, the standard error of cross-validation) are used as the main quantitative criteria (11.

The features of implementing the proposed method on spectrometers that use the principles of Fourier spectroscopy are also considered.

The essence of the invention is that the proposed set of features allows creating a completely independent grading model on a graduated measuring device, which makes it possible to predict with high accuracy the secondary properties of unknown samples based on the results of measuring many primary, not necessarily spectroscopic, properties, which takes into account non-linear differences in the technical parameters of the calibrated and reference devices, as well as the peculiarities of the operating conditions, and the calibration model is built on the basis of data on the primary properties of the samples from the calibration set, measured on the reference device and transformed into the form as if the measurements were carried out on the calibrated device. The type of transformation of the measurement results of the calibration set samples into a type equivalent to the measurement results on the calibrated instrument is determined from the measurements of the calibration transfer sample set on both instruments, and the calibration transfer set consists of a much smaller number of samples than the calibration set. The samples from the calibration transfer kit provide significant differences in measurement results across the entire range of primary properties on both the reference and calibrated instruments. The use of a set of samples for the transfer of graduations allows to determine the non-linear relationship between the results of measurements of the same samples on different devices by means of correlation analysis using regression methods. In addition, since the created grading model is completely independent and its construction uses the results of measurements of the primary properties of the samples of the grading set, adjusted to the type of the graded device, the applicability of the constructed grading model for the analysis of an unknown sample can be assessed by standard methods using statistical methods for determining data outliers, for example, by determining the Mahalanobis distance. In order to increase the accuracy of the analysis, the calibration model can be supplemented by measuring additional calibration samples on a calibrated device.

In addition, it is proposed to use the normalization procedure using various types of mathematical refinement of measurement results and data regarding secondary properties (reference data), which allow taking into account the effects of interfering factors, such as differences in sample preparation and sample condition.

The essence of the claimed invention is explained by the drawing, where Fig. is a schematic representation of the claimed method in the form of a flow chart.

The proposed method of creating independent grading models can be used for any measuring devices, where based on the results of multiple measurements of primary properties, the values of parameters that characterize some secondary properties are determined, in particular for various types of spectrometers, for example, for BiK and IR spectroanalyzers , which measure the absorption of light radiation by the sample at different values of the radiation wavelength. The results of such measurements are usually called spectral data or simply spectra. Let's consider the application of the proposed method on the example of spectrometers for analyzing the chemical composition of a sample. However, it is worth emphasizing once again that the field of application of the claimed method is not limited to spectroscopy, and in the following description spectrometers are used only as the most illustrative example.

As already mentioned, the calibration model determines the relationship between the measurement results, the spectrum, in the case of a spectrometer, and the properties of the sample being analyzed.

It should be noted that often the properties of the sample being analyzed are compared not directly to the measurement results, but to the spectral data that have already undergone the normalization procedure (previous mathematical refinement). For example, spectrum smoothing, baseline subtraction, or differentiation can be performed. The type of preliminary mathematical processing when performing the normalization procedure is selected based on the criterion of maximum accuracy in determining the secondary properties being analyzed, therefore, the mathematical operations performed must transform the spectral data in such a way that in the transformed spectral data the influence of the studied properties is manifested in the most obvious form and summarized to a minimum the influence of side factors associated with parasitic scattering and features of sample preparation. The same mathematical refinement is applied to all spectra of the calibration set samples. That is, if before the preliminary mathematical processing the type of spectra changed slightly when the studied properties of the samples changed, then after the normalization procedure, the transformed spectral data have pronounced changes even with minor changes in the analyzed properties. The statistical characteristics of the grading model are used as criteria for assessing the accuracy of the prediction, such as the standard error of calibration (5ES), the standard error of validation (SEM) and the standard error of cross-validation (ZESM) (1|. The most common type of mathematical refinement in spectral analysis is finding weighted averages of the values of the spectral data (|8|), which reduces the number of degrees of freedom in the grading model by 1. In this refinement, the spectrum averaged over the entire grading set is found and subtracted from each individual spectrum of the grading samples. Similarly, the weighted average values of the reference data are found. Then at in the analysis of an unknown sample, before applying the constructed gradation model, the spectrum averaged over the gradation set is also subtracted from the measured spectrum.

In order to create a calibration model for a spectrometer, measurements of spectral data are first made for a large set of samples (a calibration set). Samples of the calibration set for spectral analysis are selected according to the following criteria (1): a) samples must contain all chemical components that are planned to be analyzed; b) the range of changes in the concentration of the analyzed components in the samples of the calibration set should exceed the range of changes in the unknown samples being analyzed; c) the amount of change in the concentration of chemical components from sample to sample should be evenly distributed over the entire range of changes; d) the number of samples should ensure finding, using statistical methods, mathematical relationships between spectroscopic data and the concentration of individual chemical components. The determination of the samples falling out of the grading set is carried out using statistical analysis of emissions, for example, by calculating the Mahalanobis distance (1), which is defined as: r is a vector corresponding to the spectrum of one sample. The Mahalanobis distance shows how many degrees of freedom this sample contributes to the grading model. On average, each grading sample should contribute K/t, where K is the number of variables in the regression, t is the number of samples in the grading set. Samples with O25ZK/t should be excluded from the calibration set.

A large value of the Mahalonobis distance means that the spectrum of this sample almost completely determines one of the regression coefficients, which makes the model unstable. This can happen when, for example, the homogeneity and evenness of the distribution of the properties of the gradation samples being analyzed is violated in the range in which they change, that is, when the composition of the sample is significantly different from other samples in the gradation set. The calibration set should also exclude samples, the values of the analyzed properties, which, determined using the constructed model, are significantly different from the values given by the reference method. These samples are determined from Student's differences, calculated according to the formula: vi i. VES y-o2 8)

here ei is the difference between the value of the concentration of the chemical component or the analyzed property obtained with the help of the calibration model, and the reference value for the i-th calibration sample, ZES is the standard error of calibration (1), 07; - Mahalanobis distance for the ith grading sample.

Differences according to the Student should be evenly distributed according to the normal law. The magnitude of the discrepancy is compared with the Student coefficient, for a confidence probability of 0.95 and the number of degrees of freedom t-

K. If the difference exceeds the coefficient, the sample is excluded from the calibration set.

The studied properties of the samples of the calibration set are known in advance or are measured in a reference way, for example, using traditional chemical methods using reagents.

Since optical measurements in spectral analysis are carried out at a given volume of the sample, which is determined by the length of the optical path, it is desirable that the reference data be expressed in volumetric units.

High demands are placed on the accuracy and reproducibility of the reference method, because the accuracy of the spectral analysis directly depends on it. The accuracy of the reference method can be increased by repeated measurement and averaging of the reference data.

After measuring the spectral characteristics of the samples of the calibration set, a multidimensional calibration model can be created on the reference device. For this purpose, well-known mathematical methods of regression analysis are used, such as multivariate linear regression (MI ER), principal component analysis (PCA), fractional least squares method (FR5) or neural network method (NNM). Then, by measuring the spectrum of the unknown sample on the reference instrument and using the created calibration model, we can determine the properties being analyzed, for example, the concentration of one or more chemical elements, the percentage of protein, fat or starch, etc.

The created grading model allows you to predict the properties of the samples with high accuracy by measuring their spectra on the spectrometer, which was used to measure all the samples of the grading set.

When using a different spectrometer, even of the same type, the accuracy of predictions using a calibration model created on a different device is significantly reduced, which is associated with variations in the technical characteristics of spectrometers and different operating conditions. In addition, it may turn out that changes in the spectral data of the same sample, measured on different devices, go beyond the scope of the constructed grading model, which is determined by the maximum permissible value of the Mahalanobis distance. Then the calibration model created on the reference device cannot be used for analysis at all. Thus, in order to accurately predict the properties of unknown samples, each instrument must have its own independent calibration model, which takes into account non-linear differences in the characteristics of the instruments and gives a given accuracy of the analysis, and also allows to evaluate the applicability of the model for the analysis of an unknown sample using statistical methods for determining emissions, for example by determining the Mahalanobis distance.

In addition, during operation, the technical characteristics of the devices can change, which can also lead to a decrease in the accuracy of predictions and the need to build a new calibration model.

The claimed method makes it possible to create completely independent calibration models for different devices and to carry out corrections of an already created calibration model without measuring a full set of calibration samples on a calibrated device. To create a new calibration model, spectral data measured on a reference device are used, but transformed into a form equivalent to measurements on a calibrated spectrometer. The field of application and stability of the new grading model are analyzed on the basis of transformed spectral data. Since all the data from the measurement results of the calibration set samples are converted into a form equivalent to the measurement results on the calibrated instrument, when analyzing an unknown sample on the calibrated instrument, they can be used to estimate data outliers, for example, by determining the Mahalanobias distance for the spectrum of the unknown sample measured on the calibrated instrument.

To determine the ratios of conversion of the spectral data of the samples of the calibration set into a type equivalent to the results of measurements on the calibrated device, a set of samples is used, not necessarily with known properties that are analyzed, which provide the maximum possible variations of the measured spectral data, hereinafter referred to as a set for the transfer of calibrations. The spectrum of each sample from the calibration transfer set is measured on both reference (where the spectra of the calibration set samples were measured) and calibrated (for which a new calibration model is created) instruments. By correlating the spectral data for samples from the calibration transfer set, measured on the reference and calibrated instrument, relationships are found that make it possible to convert the spectra measured on the reference instrument into the form as if the measurements were carried out on the calibrated instrument and take into account non-linear discrepancies in the results of the measurements of the same samples on different devices. Both direct measurement results and spectral data that have undergone the normalization procedure, which consists in preliminary mathematical processing, can be used for correlation, while the same mathematical transformations are used for all measured spectra.

Mathematical transformations should ensure the detection of clear differences in spectral data measured on different devices, which will provide a more accurate definition of expressions for the transformation of spectral data measured on a reference device to a form equivalent to the results of measurements on a calibrated device.

Once the expressions for the transformation of the spectral data have been found, the spectral data for each sample from the calibration set can be converted to the form corresponding to the measurements on the calibrated instrument.

Next, using the standard mathematical methods of multivariate regression analysis (MI A, RSA, RIS, etc.) based on the transformed spectral data, a calibration model for the calibrated device is created.

After that, the properties of the unknown sample can be determined from measurements of spectral data on a calibrated instrument using a new independent calibration model.

In the proposed method, most of the calculations for the transformation of spectral data are performed at the stage of creating a grading model, and not at the sample analysis (there is no need for time-consuming conversion into a form equivalent to the results of measurements on a reference device), which allows to reduce the analysis time.

It should also be noted that the claimed method creates a completely independent calibration model on each calibrated device, although measurements of the calibration set of samples are carried out only once.

The transformation of spectral data for each sample of the calibration set into a form equivalent to the results of measurements on the calibrated device allows to search for samples that fall out of calibration for this specific calibrated device, which guarantees the stability of the created model.

When analyzing unknown samples, the independence of the gradation model makes it possible to evaluate the results of emission measurements in spectral data, for example, using Mahalanobis statistics, which allows you to assess the applicability of the created gradation model and the expected accuracy of the sample analysis.

To transfer the spectral data of the calibration set to the calibrated instrument, a specially selected calibration transfer sample set is used, the number of samples in which is much smaller than in the full calibration set, while their properties may not be known, it is important only that this sample set provides significant variation in the measured spectral data, which allow to find the expressions of the transformation.

The independence of the calibration model makes it possible to supplement and expand the calibration by measuring additional calibration samples with known (or measured by reference methods) properties that are analyzed directly on the calibrated device. Spectra of additional samples are added to the matrix of spectral data transformed into the type of a calibrated device for a complete calibration set, which can be checked by Mahalanobis statistics for the presence of outliers, which ensures the stability of the extended grading model. This expansion allows to increase the accuracy of the results of the analysis of the properties of unknown samples with a deeper consideration of the characteristic features of the graduated device, operating conditions and features of the analyzed samples (sample preparation, purity, etc.). For example, if the device measures the product at some stage of its production, all previous stages of production can affect not only the properties of the sample being analyzed, but also other properties of the product, which are reflected in changes in the measured spectral data, which can lead to inaccurate prediction of properties , which are analyzed; in order to increase the accuracy of predictions, it is possible to supplement the grading model with measurements of several additional grading samples that have passed all the previous stages of processing, the properties of which are accurately determined by the reference method. Another example can be supplementing the grading model with samples of agricultural products that are grown in a specific region or harvested in a specific harvest.

The independence of the calibration model created using the claimed method allows you to transfer the model already completed on the calibrated device to any other device, using the same method as when transferring from the reference device to the calibrated device. This is very convenient, because it allows you to accumulate calibration data, so, for example, when expanding production and launching a new line, you can use an updated calibration that takes into account the peculiarities of the production cycle and the properties of the raw materials used, and obtained on a device that works on an already operating line.

Since a complete set of spectra for all samples of the calibration set is used to create each new independent calibration set, transformed into a type of a calibrated device, this method allows the evaluation of data falling, for example, by the Mahalanobis distance, for an unknown sample being analyzed, directly on the calibrated device and determine the falling samples.

Another advantage of this method, namely the independence of the grading model, is that after the transformation of the spectral data for all samples from the grading set has been performed, these data can be subjected to the normalization procedure through additional mathematical processing. Thus, we get the opportunity to use our independent method of pre-mathematical processing on each calibrated device during the normalization procedure, which takes into account the features of each individual device, which significantly increases the accuracy of predictions. This is particularly useful when the calibration model is transferred from one type of reference instrument to another type of calibrated instrument, for example from a scanning diffraction grating spectrometer to a spectrometer that uses the principles of Fourier spectroscopy.

Note that the proposed method can also be used for upgrading one device, taking into account changes in the characteristics of the device that occur during operation (aging).

To illustrate the proposed method, we will give an example of creating independent grading models for determining food wheat quality indicators on several Infralum Ft-10 spectrometers located at different elevators in the Krasnodar Territory. This type of spectrometer uses principles

Fourier spectroscopy in the near infrared region of the spectrum (NIR). However, we emphasize once again that the given example is used only for illustration and a clearer understanding of the basic principles of the proposed method and in no way limits the scope of this invention.

First, the spectra of the samples of the calibration set are measured on the reference spectrometer. In spectrometers of the Infralum Ft-10 type, the measured spectra of the samples undergo the following normalization procedure, which takes into account the features of the devices that work on the omission and use the principles of Fourier spectroscopy.

The spectrum averaged over the entire calibration set is calculated.

M

Mk i-i v/- mm (10) where M is the number of samples in the calibration set, | - serial number of the wavelength at which measurements were made, В'! - measured spectral data for the i-th sample at the |-th value of the wavelength. The averaged spectrum is subtracted from each spectrum of the calibration set, thus the weighted average values of the spectral data are found.

action of Ki (17)

Similarly, weighted average values for reference data of grading samples are found. After finding the weighted average values, the spectral and reference data can be subjected to a deviation scaling procedure, in which the value at each point on the spectrum is divided by the standard deviation of the values at that point over the entire calibration set, where the standard deviation is calculated by the formula

M

(Fig

AMS sho (12) d'- M

In another version of the preliminary mathematical processing of the spectral data, the spectra are normalized by the root mean square deviation. At the same time, the arithmetic average over all wavelengths is calculated for each spectrum from the calibration set.

Hn)

In Vir 0-1 (13) where p is the number of wavelengths at which measurements are made. Then, the arithmetic mean is calculated from the values at each spectral point and the resulting difference is normalized by the root mean square deviation for the given spectrum.

K-t

R - 14

UVI -tv- p di'ismm. (and

If the baseline alignment is performed during the normalization procedure, then the spectral data are approximated by a second degree polynomial. ub)khatnaghnazh? (15) by writing expression (15) in matrix form, we get

B-a:x 1 hee hee

Uch ' 2 x x

Uha) I 2 a! uiha) kt ha ha a-|a" (16) I az

U(хр) 2 т ши ее р-

Approximation coefficients are calculated according to the formula.

A-khihu"he where X! is the transposed matrix X. After finding the approximation coefficients at each spectral point, the corresponding value of the approximating polynomial is subtracted.

After performing the procedure of normalization of the results of spectral measurements, the obtained spectral data are compared with the known, also normalized, properties of the samples of the calibration set, from which the mathematical relationships between the spectral data and the properties of the samples, known from the reference analysis, are found. These ratios determine the calibration model for the reference device.

As we noted earlier, the type of mathematical processing of spectral data during normalization is chosen based on how accurately the gradation model created with this type of data processing predicts the properties of the unknown sample, and statistical parameters of the gradation model are used as accuracy criteria.

One of these parameters is the standard error of calibration (ES), which gives an estimate of how well the properties of the samples, predicted on the basis of spectral measurements using this grading model, agree with the properties determined by the reference method.

M i-i et 17 5ES-1-! where e-u-ui is the grading error for the i-th sample of the grading set, y; - expected properties, U; - properties determined by the reference method, a-M-K - the number of degrees of freedom of the grading model, M - the number of grading samples, K - the number of variables in the grading model, which depends on the mathematical method c used to build the model.

To assess the stability of the model, a validation procedure is performed (1|. The standard error of cross-validation (SESM) allows you to estimate the maximum number of degrees of freedom that should be used when creating a model.

For assessment

In ZESM, one or more calibration samples are removed from the spectral data matrix and a model is created without these samples. The created model is then used to estimate the analyzed properties of the extracted samples. The process is repeated until each sample from the calibration set is excluded at least once.

Mi 2 mo is U (18) 5ZESU- M 1 where Tom is a vector containing cross-validation estimates.

Validation according to the additional set is determined by the parameter of the standard error of validation (SEM), which characterizes the deviation from the reference values when analyzing the samples of the additional set. n |! 2 where m) (19)

FEM! where au is the total number of reference values of the analyzed parameter for all spectra of the additional set,

In /- reference values of the analyzed component for the ith spectrum of the additional set

AND! m. predicted values of the analyzed component for the ith spectrum of the additional set.

The main characteristics of the initial grading, created from 145 food wheat samples on the reference device, are shown in Table 1.

Table 1

Results of calibration of the reference device gluten | 0.62 | 0.69 | 0.65

To create new independent calibration models on calibrated instruments, it is necessary to have a set of transfer samples. In the experiments, several samples were selected from the calibration set. Note, however, that the samples in the transfer set in general may not belong to the calibration set. Two separate transfer sets were selected.

The first set was selected based on the total parameter |8|, i.e. samples with the maximum and minimum values of the parameter for any indicator (for example, protein) were selected from the grading set.

Better transfer of gradations is achieved when to these samples are added those that have extreme values of 5sogez and on other indicators (for example, for moisture and gluten). 10 transfer samples were selected and used to construct independent calibration models on 14 instruments.

In the second case, the samples were selected so that their reference data were evenly distributed over the entire range. In this case, 10-16 samples are enough to create independent grading models.

A successful option was the transfer of spectral data of the calibration set from the reference device to five calibrated devices for protein and gluten. When the number of samples is less than 10 or more than 20 values

ZEM for new grades was getting worse.

According to the claimed method, the same calibration transfer samples were measured on all calibrated instruments. After that, by correlating the spectral data of the reference and graduated instruments, expressions were found for converting the results of spectral measurements on the reference instrument into the type of graduated instruments. A characteristic feature of InfralumM Ft-10 spectrometers, which use the principle

Fourier - spectroscopy, is that due to the design features of the devices, the measured spectra have the same constant values of the wavelengths (wave numbers) at which the measurements are made, which is provided by the synchronizing laser (8). This fact greatly simplifies the method of finding mathematical ratios for converting spectral data measured on a reference device into a form equivalent to the results of measurements on a calibrated device. In the simplest form, these relationships can be determined by the method of linear regression by comparing the results of measuring spectral data for samples from a set for the transfer of calibrations made on the reference and calibrated devices.

Vzugat"chna"t (20) de VZ; - spectral data values measured on a calibrated device (i-th wavelength, Y-th sample from a set for transferring calibrations), A" - similar spectral data measured on a reference device.

Spectral data can be subjected to the normalization procedure (preliminary mathematical processing), but completely the same transformation, both for the reference and for the calibrated devices. Regression coefficients are determined by the method of least squares. 2

Jan 5 Tue B t Fri t? | St

Mk ku ak tu aku ek | IN shi 1-1 i- i. other i-i a'-

s s s o ; with 7

E NN in SHENNY Y: SU Cho . i-1 i- i- i- i-1 a'- where c is the number of samples in the set for transferring graduations.

After finding the regression coefficients, the spectral data for each sample from the graduated set are transformed into the form corresponding to the measurements on the graduated instrument. Next, a new graded model is created based on the transformed data of the graded set. The created independent model on each graduated device underwent a standard validation procedure (1|, where the main statistical parameters of the graduated model were determined.

Table 2 shows the data on the creation of graduations for food wheat, obtained using samples for transfer, selected on the basis of the parameter z5soge for 14 graduated devices.

The obtained results demonstrate the high accuracy of predicting the properties of an unknown sample when using the proposed method of creating independent grading models.

In conclusion, we note once again that the field of application of the claimed method is not limited

Fourier spectroanalyzers or spectrometers of another type. The proposed ideology can be applied to various devices, where some properties of the sample are determined from multiple measurements of other properties.

Table 2

The results of creating gradations based on transfer samples selected based on the BSOE parameter

VES No PV KZ PVL NBN WE BI PI NBN

Sample number value. | master 470 13.94 14.09 14.07 | 13.83 | 13.88 x x 14.09 471 13.29 13.89 14.11 | 13.74 | 13.83 | 13.94 | 13.82 | 14.05 472 12.66 12.88 12.90 | 12.55 p.m 12.57 p.m 12.64 | 12.76 | 12.72 473 12.53 12.62 12.72 | 12.61 | 12.40 p.m 12.48 p.m 12.29 | 12.59 474 13.11 12.71 13.15 | 12.75 | 12.71 | 12.83 | 12.79 | 12.98

Protein 475 13.86 14.17 14.27 | 13.90 | 13.98 | 13.87 | 13.88 AND 1413 476 12.01 12.06 12.40 | 12.21 | 11.82 | 12.17 | 12.08 | 12.33 477 13.06 13.55 13.62 | 13.41 | 13.38 | 13.36 | 13.60 | 13.59 478 12.28 12.61 12.71 | 12.41 | 12.43 p.m 12.30 p.m 12.61 | 12.69 479 12.78 12.60 12.85 | 12.44 p.m 12.52 | 12.38 p.m 12.51 | 12.73

LAND | | 034 | 031 | 029 | 031 | 0.33 | 038 | 0.93 47 23.60 23.29 | 22.96 | 23.15 | 23.57 x x 23.47 471 23.90 23.03 | 23.00 | 22.65 | 23.24 | 23.70 | 23.26 | 23.32 472 20.00 20.41 20.33 | 19.88 | 20.42 | 20.38 | 20.60 | 20.18 473 19.10 18.49 18.98 | 19.28 | 18.98 | 19.22 | 18.28 | 18.90 474 20.00 20.30 | 20.81 1 20.53 | 20.51 | 21.18 | 20.83 | 20.80

Gluten 475 23.80 23.62 | 23.48 | 23.46 | 23.63 | 23.65 | 23.45 | 23.48 476 17.80 18.96 19.05 | 19.25 | 18.45 | 19.31 | 19.05 | 19.27 477 21.60 22.44 | 21.99 1 22.18 | 22.21 | 22.13 | 22.63 | 22.14 478 19.30 19.18 18.87 | 18.87 | 19.17 | 19.05 | 19.77 | 19.16 479 18.70 19.05 19.08 | 18.62 | 19.16 | 18.88 | 19.01 | 19.19 vm | yuyu yu 1 065 | 082 | 1l4 | 072 | 0.76 | 0.65 | 078 470 50.00 49.96 | 49.39 | 49.81 | 50.32 x x 49.74 471 50.00 50.72 | 49.80 | 49.11 | 50.05 | 50.59 | 50.21 | 50.09 472 47.00 49.06 | 47.65 | 47.82 | 48.29 | 48.20 | 48.48 | 48.11 473 45.00 45.71 46.57 | 46.68 | 45.94 | 46.70 | 45.09 | 46.19 474 46.00 49.05 | 48.15 | 48.60 | 48.59 | 48.50 | 48.92 | 48.38

Vitrification 475 50.00 50.64 | 50.28 | 50.56 | 50.58 | 50.09 | 51.16 | 49.76 476 50.00 48.24 | 47.48 | 47.97 | 46.85 | 48.10 | 48.11 | 47.98 477 45.00 50.90 | 49.75 1 50.22 | 50.28 | 50.29 | 50.87 | 49.70 478 47.00 47.27 | 46.17 | 46.61 | 47.51 | 47.37 | 47.64 | 46.79 479 48.00 46.58 | 45.78 | 46.00 | 45.81 | 46.27 | 46.06 | 46.13 7 5EM 17777717 237 | 230 | 2.36 | 241 | 2.36 | 2.82 | 2.06 470 11.50 11.03 10.92 | 11.04 | 10.94 x x 10.95 471 11.00 11.06 10.96 | 11.08 | 11.01 | 10.99 | 11.04 | 11.01 472 11.00 10.91 10.96 | 10.98 | 10.94 | 10.96 | 10.95 | 10.98

Humidity 473 11.50 11.48 11.31 | 11.42 | 11.36 | 11.48 | 11.50 | 11.33 474 11.00 10.89 10.80 | 10.88 | 10.85 | 10.85 | 10.91 | 10.88 475 11.00 11.09 11.04 | 11.12 | 11.07 | 11.15 | 11.12 | 11.06 476 11.00 11.41 11.37 | 11.35 | 11.43 | 11.38 | 11.41 | 11.33

477 10.50 10.76 10.78 | 10.71 | 10.74 | 10.83 | 10.69 | 10.73 478 12.00 11.71 11.55 | 11.63 | 11.59 | 11.73 | 11.63 | 11.60 479 12.00 11.82 11.66 | 11.88 | 11.77 | 11.86 | 11.82 | 11.74 7 5EM | 7777/7025 | 033 025 | 030 | 021 | 021 | 0.28 ov WE FULL PY PNYA NOYA NI

Sample number 470 13.98 13.98 14.11 | 14.13 | 14.16 | 14.27 | 14.21 | 14.12 471 14.29 14.09 14.24 | 14.14 | 14.12 | 14.24 | 14.16 | 14.11 472 12.82 12.78 12.86 | 12.74 | 12.75 | 12.70 p.m 12.82 | 12.76 473 12.82 12.58 12.75 | 12.75 | 12.82 | 12.69 | 12.79 | 12.68 474 13.02 12.82 13.04 | 13.04 | 13.09 | 13.02 | 13.04 | 13.05

Protein 475 14.28 13.99 14.17 | 14.12 | 14.28 | 14.29 | 14.16 | 14.25 476 12.38 12.02 12.04 | 12.08 | 12.23 | 12.24 p.m 12.30 112.27 "477 13.60 13.58 13.69 | 13.76 | 13.68 | 13.73 | 13.64 | 12.65 478 12.74 12.74 12.76 12.76 | 12.81 | 12.85 | 12.68 | 12.67 | 12.84 479 12 23.26 | 23.33 | 23.36 | 23.39 471 23.54 23.20 23.21 | 23.55 | 23.07 | 23.22 | 23.17 | 23.46 472 20.13 20.27 | 20 474 20.30 20.08 20.51 | 20.91 | 20.70 | 20.39 | 20.56 | 20.40

Gluten 475 23.50 23.22 23.17 | 23.45 | 23.49 | 23.42 | 23.15 | 23.71 476 18.84 18.38 17.99 | 18.54 | 18.58 | 18.60 | 18.62 | 18.57 477 21.82 21.96 22.17 | 22.97 | 22.27 | 22.13 | 22.07 x 478 18.58 19.13 1900 | 19.56 | 19.31 | 18.61 | 18.49 | 19.48 479 19.01 18.76 18.74 | 19.24 | 19.12 | 19.00 | 19.12 | 20.19 /// 85EM | 068 | 069 | 0.64 | 0.65 | 0.65 | 0.60 | 0.70 | 0.65 470 49.29 50.22 50.25 | 50.85 | 50.38 | 50.21 | 50.28 | 51.21 471 50.47 50.31 50.30 | 50.04 | 50.07 | 50.18 | 50.20 | 50.76 472 48.74 48.14 | 48.23 | 48.16 | 48.17 | 48.11 | 47.82 | 49.03 473 46.19 46.44 | 46.09 | 46.43 | 46.47 | 46.14 | 46.65 | 46.61 474 48.49 47.88 48.40 | 49.01 | 48.87 | 47.95 | 48.29 | 48.66

Vitrification 475 50.26 50.23 50.33 | 50.43 | 50.45 | 50.46 | 49.97 | 51.38 476 47.48 47.63 46.85 | 47.31 | 47.46 | 47.42 | 47.37 | 48.22 477 50.49 49.80 50.44 | 50.80 | 50.42 | 49.99 | 50.57 x 478 45.55 46.98 46.87 | 47.18 | 46.81 | 46.14 | 45.99 | 47.08 479 45.45 45.90 45.38 | 45.85 | 46.18 | 45.94 | 45.35 | 45.22 470 11.08 10.97 10.98 | 10.95 | 10.96 | 10.89 | 10.96 | 11.09 471 10.95 10.99 11.00 | 10.97 | 10.99 | 10.94 | 10.80 | 11.16 472 10.90 10.99 10.89 | 11.03 | 10.90 | 10.87 | 10.85 | 11.09 473 11.29 11.38 11.33 | 11.35 | 11.33 | 11.35 | 11.34 | 11.48 474 10.78 10.82 10.81 | 10.80 | 10.82 | 10.71 | 10.73 | 11.22

Humidity 475 11.02 11.07 10.98 | 11.04 | 11.01 | 10.99 | 11.04 | 11.11 476 11.29 11.42 11.36 | 11.38 | 11.36 | 11.27 | 11.32 | 11.46 477 10.72 10.77 10.74 | 10.75 | 10.71 | 10.65 | 10.67 x 478 11.58 11.62 11.51 | 11.61 | 11.55 | 11.45 | 11.40 | 11.51 479 11.65 11.75 1171 | 11.72 | 11.71 | 11.61 | 11.55 | 11.51 7 The spectrum was not registered.

Sources of information: 1. ABTM ziapaaga, E 1655 - 00, Rgasiisez og Ipitagei Miiimagiagie Otsapiiaime Apaiuviv. 2. US patent application Mo 4 944 589, IPC 201U3/18, published 31.07.1990 3. US patent application Mo 6 615 151, IPC C201M015/06, published 02.09.2003 4. US patent application Mo 4 866 644, IPC 201M37/ 00, published 12.09.1989 5. US patent application Mo 5 459 677, IPC C201M021/01, published 17.10.1995 6. European patent application EP 0 663 997 B1, IPC 201Mm021/27, published 17.10.1995. 7. US patent application Mo 5 347 475, IPC (0019003/02, published on 13.09.1994 8. Infralum Ft-10 operation manual, 152.00.00.00.РЗ

r and MN KNT mu

Pi Z I p ions «nn - - and en

Washed away the smoke of the set of the day of transfer of hailstones! nachztornomu and graduable prnnadah and | Noreapization procedure Oh God! ra | of a set of samples with r Correlation | Information about burning, burning, etc alalvostny and he V nn wine

M nya | Measurement of samples

AJ BA of their pre-production set - | in the supporting place, the result of the transformation was stolen from Pbodvan by Maopodnemu au Onomaly

Goes PVVDUIOVONNA, sia ET sn! Conversion of the results of a sample string: with Mpuyuvannoo naboruu type traduovannya pinkalu pon PI i

Z te na skin kit in z kozh Z s zhi z yuyu yuku shk Definition of matamatnyh in the limiter and Z

VK she

EU 7 Vaidatsiya C" he one r rent nya, i. and THE END IS YET